1. Field of Invention
This invention relates to determining the magnitude and phase of an ac signal in less than one cycle even with dc offset present. More particularly, the invention discloses a method and apparatus for generating samples of sinusoidal current or voltage which are then used in a mathematical solution described in the invention to determine magnitude and phase. It is particularly useful in the presence of dc offset. Use of relatively few samples with a fast response time is disclosed. The invention is described in connection with protective relays.
2. Background Information
It is often necessary in electric power transmission systems to compute the magnitude and phase of the line current or voltage. Such computations are performed, for example, in protective relays.
In the case of protective distance relays, components are placed at each terminal of the protected line segment, these components analyze line currents and voltages to determine the location of a fault and trip circuit breakers at the respective terminals to isolate a fault determined to be between terminals. The invention can be used in such a relay system to measure the current and voltage.
The calculation of line voltage and line current as well as the phase is often made more difficult by the presence of dc offset. DC offset, such as could occur when a transformer is brought on line, can cause false trips in certain protective relays.
It is known that transient exponential noise can be reduced by substituting a compensated signal for the noise using linear approximations of the exponential component. Pending U.S. Patent Application Ser. No. 207,354 discloses a method and apparatus for reducing transient exponential noise in a sinusoidal signal by determining from digital samples of the signal the slope and initial ordinate value of a linear approximation of the transient exponential noise. The invention derives compensated values of current and voltage directly from digital samples of the waveform, and provides such compensated values from the beginning of the transient within one-half cycle of transient initiation plus one additional sample interval The compensation involves deriving the slope of the linear approximation of the exponential component of the transient by adding the magnitudes of each of a first pair of digital samples for instants spaced one-half cycle apart to produce a sum, subtracting from this sum the magnitude of each of a second pair of digital samples also one-half cycle apart and spaced from a corresponding one of the first pair of digital samples by a preselected number to produce a result.
The ordinate value of the linear approximation of the exponential component of the transient is determined by calculating the average of the magnitudes of the first pair of digital samples and adding to that average the sum of the magnitudes of the first pair minus the sum of the magnitude of the second pair divided by the number of intervals between corresponding samples in the first and second pairs of samples.
The method and apparatus discussed above does not involve calculation of magnitude and phase from alternate samples which are spaced by ninety electrical degrees of the waveform. In addition, there remains a need for a method and apparatus for accurate calculation of magnitude and phase in the presence of dc offset using relatively few samples and having a response time of less than one-half cycle.
As can be seen from the above, there is a need in many applications for a technique for rapidly analyzing waveforms, preferably in less than one power cycle. Further, the calculation must be made on-line with relatively modest hardware if it is to be cost competitive.